Combining multiple emergent correlated properties such as superconductivity and magnetism within the topological matrix can have exceptional consequences in garnering new and exotic physics. Here, we study the topological surface states from a noncentrosymmetric α-BiPd superconductor by employing angle-resolved photoemission spectroscopy (ARPES) and first principle calculations. We observe that the Dirac surface states of this system have several interesting and unusual properties, compared to other topological surface states. The surface state is strongly anisotropic and the inplane Fermi velocity varies rigorously on rotating the crystal about the y-axis. Moreover, it acquires an unusual band gap as a function of ky, possibly due to hybridization with bulk bands, detected upon varying the excitation energy. Coexistence of all the functional properties, in addition to the unusual surface state characteristics make this an interesting material. α-BiPd is recently synthesized with all the aforementioned properties obtained intrinsically, and thus provides the long-sought material for new experiments and applications. So far, there have been few works on this material, mainly studying the magnetic and transport phenomena [9][10][11]. Again, for the spectroscopic investigations, there is only one ARPES [12] and one scanning tunnelling spectroscopy (STS) study [13]. The ARPES work reported the electronic structure of this compound with the detection of topological Dirac cone at -0.7 eV below the Fermi level (E F ), without detailing the properties of Dirac cone, while the STS work reported the states above the Fermi level.In this paper we report several interesting and unusual properties of the topological Dirac states present on the surface of this noncentrosymmetric α-BiPd superconductor by employing ARPES and first principle calculations. We detect the surface states that are having a Dirac node at a binding energy of 0.7 eV below Fermi level (E F ) at the Γ point dispersing along the Γ − X high symmetry line. Upon varying the photon energy, we notice surface states that are gapped as a function of k y at the node due to a possible hybridization with bulk bands, a unique feature of the surface state that is not disclosed in this compound so far. Upon varying the photon polarization we identify the orbital character of the detected bands.We further show that the Dirac fermions in α-BiPd are highly anisotropic on rotating the crystal about the y-axis such that, in going from Γ−X to Γ−Z the massless linear dispersive Dirac states become flat dispersive massive fermions. Therefore, the Dirac states found in this compound are of one dimensional (1D) character which could provide a natural route for the quantum wires. In general, the Dirac states found on the surface of 2D compounds such as graphene [14] [24]. Unusual band structure of this material, surface state is gapped and asymmetric, make this a unique compound which will attract tremendous future research interests.Single crystals of stoichiometric α-BiPd were g...